Before switching to a new device, you'll want to make sure you have already created a Calm account to ensure no data is lost. Once you've created a Calm account on your old phone, any session history or subscription information on that device will become synced to your Calm account so you can access it from other devices.
Switching from Android to iOS
Because your Calm subscription was purchased through your Google Play account and your new phone no longer has Google Play on it, you will need to cancel your current Calm subscription within your Google Play account. To do so, head to the Google Play Store website, click 'Account' in the left-hand menu, and scroll down to the Subscriptions section. If you have any trouble, please see this support article for more details: https://support.google.com/googleplay/answer/7018481
Switching from iOS to Android
Because your Calm subscription was purchased through your iTunes account and your new phone no longer has iTunes on it, you will need to cancel your current Calm subscription within your iTunes account. You can do so through iTunes on another device or by contacting Apple directly at https://getsupport.apple.com/.
Once your subscription expires, you'll need to renew on your new device in order to keep enjoying Calm Premium.